Exotic R^4 and quantum field theory

Recent work on exotic smooth R^4's, i.e. topological R^4 with exotic differential structure, shows the connection of 4-exotics with the codimension-1 foliations of $S^{3}$, SU(2) WZW models and twisted K-theory $K_{H}(S^{3})$, $H\in H^{3}(S^{3},\mathbb{Z})$. These results made it possible to explicate some physical effects of exotic 4-smoothness. Here we present a relation between exotic smooth R^4 and operator algebras. The correspondence uses the leaf space of the codimension-1 foliation of S^3 inducing a von Neumann algebra $W(S^{3})$ as description. This algebra is a type III_1 factor lying at the heart of any observable algebra of QFT. By using the relation to factor II, we showed that the algebra $W(S^{3})$ can be interpreted as Drinfeld-Turaev deformation quantization of the space of flat SL(2,\mathbb{C}) connections (or holonomies). Thus, we obtain a natural relation to quantum field theory. Finally we discuss the appearance of concrete action functionals for fermions or gauge fields and its connection to quantum-field-theoretical models like the Tree QFT of Rivasseau.Comment: 15 pages, 2 figures, Based on the talk presented at Quantum Theory and Symmetries 7, Prague, August 7-13, 2011, JPconf styl

Thermal Dissociation Behavior and Dissociation Enthalpies of Methane–Carbon Dioxide Mixed Hydrates

Replacement of methane with carbon dioxide in hydrate has been proposed as a strategy for geologic sequestration of carbon dioxide (CO{sub 2}) and/or production of methane (CH{sub 4}) from natural hydrate deposits. This replacement strategy requires a better understanding of the thermodynamic characteristics of binary mixtures of CH{sub 4} and CO{sub 2} hydrate (CH{sub 4}-CO{sub 2} mixed hydrates), as well as thermophysical property changes during gas exchange. This study explores the thermal dissociation behavior and dissociation enthalpies of CH{sub 4}-CO{sub 2} mixed hydrates. We prepared CH{sub 4}-CO{sub 2} mixed hydrate samples from two different, well-defined gas mixtures. During thermal dissociation of a CH{sub 4}-CO{sub 2} mixed hydrate sample, gas samples from the head space were periodically collected and analyzed using gas chromatography. The changes in CH{sub 4}-CO{sub 2} compositions in both the vapor phase and hydrate phase during dissociation were estimated based on the gas chromatography measurements. It was found that the CO{sub 2} concentration in the vapor phase became richer during dissociation because the initial hydrate composition contained relatively more CO{sub 2} than the vapor phase. The composition change in the vapor phase during hydrate dissociation affected the dissociation pressure and temperature; the richer CO{sub 2} in the vapor phase led to a lower dissociation pressure. Furthermore, the increase in CO{sub 2} concentration in the vapor phase enriched the hydrate in CO{sub 2}. The dissociation enthalpy of the CH{sub 4}-CO{sub 2} mixed hydrate was computed by fitting the Clausius-Clapeyron equation to the pressure-temperature (PT) trace of a dissociation test. It was observed that the dissociation enthalpy of the CH{sub 4}-CO{sub 2} mixed hydrate lays between the limiting values of pure CH{sub 4} hydrate and CO{sub 2} hydrate, increasing with the CO{sub 2} fraction in the hydrate phase

Relationship of retinal vascular caliber with diabetes and retinopathy: The Multi-Ethnic Study of Atherosclerosis (MESA)

10.2337/dc07-1528Diabetes Care313544-54